Unit 1 Basics of Geometry

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71 Terms

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Midpoint Property

If (x1, y1) and (x2, y2) are the coordinates of the endpoints of a segment, then the coordinates of the midpoint are: (X plus X divided by 2, and, Y plus Y divided by 2) Labeled as a coordinate pair (X, Y).

<p>If (x1, y1) and (x2, y2) are the coordinates of the endpoints of a segment, then the coordinates of the midpoint are: (X plus X divided by 2, and, Y plus Y divided by 2) Labeled as a coordinate pair (X, Y).</p>
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Undefined terms of Geometry

point, line, plane

<p>point, line, plane</p>
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Collinear Points

points that lie on the same line

<p>points that lie on the same line</p>
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Coplanar Points

points that lie on the same plane

<p>points that lie on the same plane</p>
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Line Segment

consists of two points called the endpoints and all the points in between them that are collinear with the two points

<p>consists of two points called the endpoints and all the points in between them that are collinear with the two points</p>
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Congruent segments

segments that have the same measure or length

<p>segments that have the same measure or length</p>
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Midpoint of a segment

the point on the segment that is same distance from both endpoints, midpoint bisects the segment

<p>the point on the segment that is same distance from both endpoints, midpoint bisects the segment</p>
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Ray

Portion of a line that contains all the points on the line that are on the same side of the first letter as the second letter

<p>Portion of a line that contains all the points on the line that are on the same side of the first letter as the second letter</p>
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Angle

Two noncollinear rays having a common endpoint.

<p>Two noncollinear rays having a common endpoint.</p>
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Adjacent Angles

two angles that share a common vertex and side, but have no common interior points

<p>two angles that share a common vertex and side, but have no common interior points</p>
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Measure of an angle

the smallest amount of rotation about the vertex from one ray to the other.

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Protractor
a geometry tool used to measure angles
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Congruent Angles

two angles that have the same measure

<p>two angles that have the same measure</p>
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Angle Bisector

a ray that contains the vertex and divides the angle into two congruent angles

<p>a ray that contains the vertex and divides the angle into two congruent angles</p>
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Counterexample
an example that proves that a statement is false
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Parallel Lines

lines in the same plane that never intersect

<p>lines in the same plane that never intersect</p>
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Perpendicular Lines

lines that intersect at right angles (90 degrees)

<p>lines that intersect at right angles (90 degrees)</p>
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Skew Lines

lines that are not in the same plane and do not intersect

<p>lines that are not in the same plane and do not intersect</p>
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Acute Angle
an angle that measures greater than 0 degrees and less than 90 degrees
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Right Angle
an angle that measures 90 degrees
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Obtuse Angle
An angle that measures more than 90 degrees but less than 180 degrees
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Straight Angle
an angle that measures 180 degrees
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Linear Pair

two adjacent angles whose noncommon sides are opposite rays

<p>two adjacent angles whose noncommon sides are opposite rays</p>
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Vertical Angles

angles formed by 2 intersecting lines; they share a common vertex not a side

<p>angles formed by 2 intersecting lines; they share a common vertex not a side</p>
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Complementary Angles
two angles whose measures have a sum of 90 degrees
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supplementary angles
two angles whose measures have a sum of 180 degrees
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Polygon
a closed figure in a plane, formed by connecting line segments endpoint to endpoint with each segment intersecting exactly two others
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Three Sided Polygon
Triangle
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Four Sided Polygon
quadrilateral
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Five Sided Polygon
pentagon
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Six Sided Polygon
hexagon
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Seven Sided Polygon
heptagon
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Eight Sided Polygon
octagon
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Nine Sided Polygon
nonagon
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Ten Sided Polygon
decagon
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Eleven Sided Polygon
undecagon
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Twelve Sided Polygon
dodecagon
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diagonal of a polygon
a line segment connecting two nonconsecutive vertices of a polygon
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convex polygon
a polygon with no diagonal outside the polygon
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Concave Polygon
A polygon that has at least one diagonal with points outside the polygon.
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congruent polygons

two polygons whose corresponding sides and angles are congruent

<p>two polygons whose corresponding sides and angles are congruent</p>
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equilateral polygon

a polygon in which all sides are congruent

<p>a polygon in which all sides are congruent</p>
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equiangular polygon
A polygon with all angles have same measure
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Regular Polygon
a polygon that is both equilateral and equiangular
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Right Triangle
a triangle that has one right angle
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acute triangle
A triangle with 3 acute angles
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obtuse triangle
a triangle with one obtuse angle
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scalene triangle
a triangle with no congruent sides
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equilateral triangle
A triangle with three congruent sides
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Isosceles Triangle
a triangle with at least two congruent sides
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<p>Trapezoid</p>

Trapezoid

A quadrilateral with exactly one pair of parallel sides

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<p>Kite</p>

Kite

a quadrilateral with two distinct pairs of consecutive congruent sides

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<p>Parallelogram</p>

Parallelogram

A quadrilateral with two pairs of parallel sides

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<p>Rhombus</p>

Rhombus

an equilateral parallelogram (all congruent sides, 2 pairs of parallel sides)

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<p>Rectangle</p>

Rectangle

an equiangular parallelogram (all congruent angles, 2 pairs of parallel sides)

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<p>Square</p>

Square

an equilateral rectangle or an equiangular rhombus or a regular quadrilateral

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Circle
The set of all points in a plane that are the same distance from a given point called the center
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Radius
The distance from the center of a circle to any point on the edge of a circle
The distance from the center of a circle to any point on the edge of a circle
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Diameter
A line segment that passes through the center of a circle and has endpoints on the circle
A line segment that passes through the center of a circle and has endpoints on the circle
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Secant
A line that intersects a circle in two points
A line that intersects a circle in two points
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chord
A segment whose endpoints lie on a circle
A segment whose endpoints lie on a circle
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Tangent
A line in the plane of a circle that intersects the circle in exactly one point.
A line in the plane of a circle that intersects the circle in exactly one point.
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point of tangency
the point where a circle and a tangent intersect
the point where a circle and a tangent intersect
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congruent circles
Two or more circles that have the same radius
Two or more circles that have the same radius
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concentric circles
2 or more coplanar circles with the same center
2 or more coplanar circles with the same center
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arc of a circle
two points on the circle and the continuous part of the circle between the two points
two points on the circle and the continuous part of the circle between the two points
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semicircle
an arc with endpoints that are the endpoints of a diameter
an arc with endpoints that are the endpoints of a diameter
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minor arc
an arc that is less than a semicircle
an arc that is less than a semicircle
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Major Arc
an arc that is greater than a semicircle
an arc that is greater than a semicircle
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Central Angle
an angle with its vertex at the center of a circle
an angle with its vertex at the center of a circle
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arc measure
the measure of the corresponding central angle
the measure of the corresponding central angle

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